Properties

Level $22$
Weight $0$
Character 22.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 6.90929754869 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.170308282\) \(a_{4}=+0.500000000\) \(a_{5}=-0.421101649\)
\(a_{6}=-0.827532923\) \(a_{7}=-0.382188210\) \(a_{8}=-0.353553391\) \(a_{9}=+0.369621476\) \(a_{10}=+0.297763832\)
\(a_{11}=+0.301511345\) \(a_{12}=+0.585154141\) \(a_{13}=-0.286765913\) \(a_{14}=+0.270247875\) \(a_{15}=-0.492818748\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.187718670\) \(a_{18}=-0.261361852\) \(a_{19}=+0.027479420\) \(a_{20}=-0.210550824\)
\(a_{21}=-0.447278027\) \(a_{22}=-0.213200716\) \(a_{23}=-1.463490275\) \(a_{24}=-0.413766461\) \(a_{25}=-0.822673401\)
\(a_{26}=+0.202774122\) \(a_{27}=-0.737737208\) \(a_{28}=-0.191094105\) \(a_{29}=+0.673324220\) \(a_{30}=+0.348475478\)
\(a_{31}=-0.044191979\) \(a_{32}=-0.176776695\) \(a_{33}=+0.352861224\) \(a_{34}=+0.132737144\) \(a_{35}=+0.160940085\)
\(a_{36}=+0.184810738\) \(a_{37}=-1.190997425\) \(a_{38}=-0.019430884\) \(a_{39}=-0.335604523\) \(a_{40}=+0.148881916\)
\(a_{41}=-1.689782975\) \(a_{42}=+0.316273326\) \(a_{43}=-0.247985149\) \(a_{44}=+0.150755672\) \(a_{45}=-0.155648213\)
\(a_{46}=+1.034843898\) \(a_{47}=-0.353434037\) \(a_{48}=+0.292577071\) \(a_{49}=-0.853932172\) \(a_{50}=+0.581717941\)
\(a_{51}=-0.219688714\) \(a_{52}=-0.143382957\) \(a_{53}=+0.280085211\) \(a_{54}=+0.521658982\) \(a_{55}=-0.126966924\)
\(a_{56}=+0.135123937\) \(a_{57}=+0.032159393\) \(a_{58}=-0.476112122\) \(a_{59}=+1.422363597\) \(a_{60}=-0.246409374\)
\(a_{61}=+0.888026580\) \(a_{62}=+0.031248448\) \(a_{63}=-0.141264970\) \(a_{64}=+0.125000000\) \(a_{65}=+0.120757599\)
\(a_{66}=-0.249510564\) \(a_{67}=-1.302407968\) \(a_{68}=-0.093859335\) \(a_{69}=-1.712734790\) \(a_{70}=-0.113801826\)
\(a_{71}=+0.688333078\) \(a_{72}=-0.130680926\) \(a_{73}=-1.237153203\) \(a_{74}=+0.842162355\) \(a_{75}=-0.962781495\)
\(a_{76}=+0.013739710\) \(a_{77}=-0.115234081\) \(a_{78}=+0.237308234\) \(a_{79}=+1.712615814\) \(a_{80}=-0.105275412\)
\(a_{81}=-1.233001440\) \(a_{82}=+1.194857000\) \(a_{83}=+1.714920847\) \(a_{84}=-0.223639014\) \(a_{85}=+0.079048641\)
\(a_{86}=+0.175351980\) \(a_{87}=+0.787996911\) \(a_{88}=-0.106600358\) \(a_{89}=-0.783419880\) \(a_{90}=+0.110059907\)
\(a_{91}=+0.109598551\) \(a_{92}=-0.731745137\) \(a_{93}=-0.051718239\) \(a_{94}=+0.249915604\) \(a_{95}=-0.011571629\)
\(a_{96}=-0.206883231\) \(a_{97}=-0.006152715\) \(a_{98}=+0.603821230\) \(a_{99}=+0.111445068\) \(a_{100}=-0.411336701\)

Showing 100 of 280 available coefficients

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